Method of aligning arm reference system of a multiple-arm measurement machine

ABSTRACT

A method of aligning arm reference systems of a multiple-arm measuring machine having at least two measuring units, each having a movable arm; the method including the steps of aligning the reference systems of the measuring units when setting up the machine, and periodically updating alignment of the reference systems by detecting, by means of one measuring unit, a reference member carried by another measuring unit and moved successively by the other measuring unit into a number of positions at an intersection of the measuring volumes of the two measuring units.

PRIORITY

This application claims priority under 35 U.S.C. 365 AND/OR 35 U.S.C.119 to PCT application no. PCT/IT2007/000641 filed on 14 Sep. 2007.

TECHNICAL FIELD

The present invention relates to a method of aligning arm referencesystems of a multiple-arm measuring machine.

BACKGROUND ART

As is known, multiple-arm measuring machines comprise two or moremeasuring units, each with its own measuring tool, which operate incoordination under the control of a common control system. The measuringunits are normally positioned with their respective measuring volumesside by side and overlapping at a small intersection, so the overallmeasuring volume of the machine is defined by the combined measuringvolumes of the individual units. Multiple-arm measuring machines of theabove type are therefore particularly suitable for measuring large-sizeparts, such as vehicle bodies or aircraft components.

In a typical embodiment, to which the following description refers forconvenience and purely by way of example, the machine comprises twohorizontal-arm cartesian measuring units located on opposite sides ofthe measuring volume, and each unit comprises a column movable along alongitudinal first axis with respect to the measuring volume, a carriagefitted to the column and movable along a vertical second axis, and anarm fitted to the carriage and movable with respect to it along ahorizontal third axis perpendicular to the first axis and crosswise tothe measuring volume.

In multiple-arm machines employing coordinate measuring units(particularly machines with two horizontal arms), aligning the cartesianreference system of one of the two arms (the secondary or “slave” arm)with respect to the other (the “primary” or “master” arm) is vital tomeasuring performance in two-arm mode.

The usual alignment method comprises measuring a sphere variouslypositioned at the intersection between the measuring volumes of the twounits, and accordingly rotating and translating the cartesian referencesystem of the secondary arm with respect to that of the primary arm.

Measuring machine performance in multiple-arm mode depends closely onthe compensation precision and dimensional stability of the individualunits, and on the precision and stability of the results of the abovealignment procedure.

The latter, in particular, is affected by deformation of both measuringunits caused by variations in ambient temperature, which may result indistortion of the geometry of both units, not entirely recoverable bythe geometric compensation procedure, and in elongation of the componentparts of the units (transducers, beams, etc.), which often results inmeasuring errors serious enough to impair performance.

Distortion of individual units also results in even serious measuringerrors in multiple-arm mode.

Frequently updating alignment of the cartesian reference systems of eachunit of a multiple-arm machine is therefore of vital importance, but inactual fact difficult, if not impossible, to do in the case of on-linemeasuring systems, which rule out a fixed floor-mounted sphere forobvious accommodation reasons.

Another factor affecting the performance of multiple-arm machines is theweight of the workpiece, which may cause significant yield of thefoundation and/or bed on which the units are installed, thus affectingthe no-load-determined alignment conditions of the units.

One way of minimizing this effect is to align the systems with theworkpiece set up in place, though often the very size of the workpieceprevents this. A “mockup” is another possible solution, but oftenunpractical and technically unfeasible, by involving additionalmovements, possibly interfering with dedicated workpiece supportingfixtures, and possibly differing considerably from the loadconfiguration of the actual workpiece. The problem with this solution isfurther compounded by the load varying with different workpieces.

The only solution to these problems lies in oversizing the foundationand/or bed, thus increasing the cost of the machine.

DISCLOSURE OF INVENTION

It is an object of the present invention to provide a method of aligningarm reference systems of a multiple-arm measuring machine, designed toeliminate the aforementioned drawbacks typically associated with knownmethods.

According to the present invention, there is provided a method ofaligning arm reference systems of a multiple-arm measuring machine, asclaimed in claim 1.

The invention (which also applies to non-cartesian machines and to otherthan two-arm multiple-arm systems) provides for periodically updatingthe alignment matrix by means of one or more reference members locatedon the structure of at least one of the measuring units and measurableby the other unit.

The reference members may be:

a) one or more calibrated spheres located on the end of one of the armsand easily accessible by the tracer on the other arm, or located on adedicated tool interchangeable with the measuring tools and housable inthe tool-change store;

b) dedicated gauges, if the machine is equipped with non-contact tracersonly, which cannot measure the above spheres easily.

By means of appropriate measuring programs activated automatically or bythe operator alongside changes in the type of workpiece or inenvironmental conditions, such as variations in temperature, theinvention provides for updating the alignment matrix, thus improvingmeasuring performance and greatly reducing cost in terms of sizing ofthe foundation and/or bed.

Moreover, the method may be applied to the actual workpiece-occupiedportion of the local volume common to both arms, thus potentiallyimproving measuring performance and also enhancing the versatility ofthe system, which can thus be used for measuring both large- andsmall-size workpieces (vehicle bodies and panels).

BRIEF DESCRIPTION OF THE DRAWINGS

A preferred, non-limiting embodiment of the present invention will bedescribed by way of example with reference to the accompanying drawings,in which:

FIG. 1 shows a schematic plan view of a two-arm measuring machine inaccordance with the present invention;

FIG. 2 shows a schematic front view of the FIG. 1 machine;

FIG. 3 shows a schematic detail of a measuring unit of the FIG. 1machine;

FIG. 4 shows a flow chart of a procedure for aligning the referencesystems of the FIG. 1 machine at the machine installation stage;

FIG. 5 shows the location of a reference member during the procedureshown in the FIG. 4 flow chart;

FIG. 6 shows a flow chart of a first operation in updating alignment ofthe reference systems of the FIG. 1 machine measuring units;

FIG. 7 shows a flow chart of a second operation in updating alignment ofthe reference systems of the FIG. 1 machine measuring units.

BEST MODE FOR CARRYING OUT THE INVENTION

With reference to FIGS. 1 and 2, number 1 indicates as a whole a two-armcartesian measuring machine.

Machine 1 substantially comprises a bed 2 defining a horizontalreference surface 3; and two horizontal-arm measuring units 4, 5 formoving respective measuring tools 6, 7 with respect to reference surface3.

Measuring unit 4 comprises a column 8 movable along a guide 9 extendingalong a longitudinal side of bed 2 and parallel to an axis X of a set ofthree coordinate axes X, Y, Z defining a reference system integral withbed 2. Guide 9 may be of any conventional type, and is only shownschematically in FIG. 1.

Measuring unit 4 also comprises a carriage 10 fitted to and movablealong column 8 along axis Z; and a horizontal arm 11 fitted to carriage10 and movable along the horizontal axis Y.

Measuring tool 6 is fitted to an end flange 12 of arm 11, preferably bymeans of a known articulated head 13, with two degrees of rotationalfreedom, for adjusting the position of measuring tool 6.

Likewise, measuring unit 5 comprises a column 15 movable along a guide16 extending along the opposite longitudinal side of bed 2 to guide 9and parallel to axis X; a carriage 17 fitted to and movable along column15 in a direction parallel to axis Z; and a horizontal arm 18 fitted tocarriage 17 and movable in a direction parallel to axis Y.

Measuring tool 7 is fitted to an end flange 19 of arm 18, preferably bymeans of a known articulated head 20 with two degrees of rotationalfreedom.

The moving parts of measuring units 4, 5 and articulated heads 13, 20are controlled by electric motors (not shown), in turn controlled by acontrol and processing unit 24 connected to known linear positiontransducers (not shown) associated with the machine axes, and to knownangular transducers (not shown) associated with articulated heads 13,20.

As shown more clearly in FIG. 3, flange 12 of arm 11 of unit 4 isconveniently fitted with a reference sphere 25 for the purpose explainedbelow.

Each measuring unit 4, 5 has its own measuring volume defined by all thepositions reachable by the measuring tool alongside variations in theposition of the machine axes. The two measuring volumes, indicated M1and M2, necessarily have an intersection I, and together define themeasuring volume M of machine 1 when operating in “two-arm” mode.

To operate in two-arm mode, the reference systems of both arms must bealigned, i.e. the measurements of both units 4, 5 must refer to a commonreference system.

Assuming the X,Y,Z reference system defined above is that of unit 4 (theprimary or “master” unit), a second x,y,z reference system may beintroduced associated with unit 5 (the secondary or “slave” unit).

Aligning the two reference systems comprises rotating and translatingthe reference system of slave unit 5 so that its axes are parallel toand have the same origin as those of the reference system of master unit4.

Mathematically, this amounts to applying a coordinate transformation τ:P=τp=T+Rp  (1)

where:

P is the three-component vector (X, Y, Z) of the master systemcoordinates;

p is the three-component vector (x, y, z) of the slave systemcoordinates;

T is a three-component translation vector (tx, ty, tz) which determinesthe position of the origin of the slave coordinate system in the mastercoordinate system; and

R is a rotation matrix (3 by 3).

When setting up machine 1, routine geometric compensation of units 4 and5 and qualification of measuring tools 6 and 7 are followed by alignmentof the reference systems of units 4 and 5, which comprises the steps of:

1) Acquiring the angular errors between the two reference systems, andso determining the coefficients of matrix R.

A simple, easily automated method of determining rotation componentsonly is as follows (FIG. 4).

The movable sphere 25, integral with arm 11, is moved successively byunit 4 along a grid defined by n positions in a plane parallel to axes Xand Z (i.e. a Y-constant plane) at intersection I (FIG. 4), e.g. ismoved into nine positions arranged in three horizontal rows (and sodefining respective Z- and Y-constant lines r1, r2, r3—FIG. 5). Thecoordinates Pi of the centre of sphere 25 in the slave system areacquired in each of the above positions, and the operation is performedfor all the positions in an automatic measuring cycle defined by blocks31 to 35 in the FIG. 4 chart.

By means of an optimization, e.g. least squares, method, it is thereforepossible to calculate the plane which best approximates the 9 points inthe x,y,z slave reference system (block 36), and calculate thedirections of axes X,Y,Z in the slave system (block 37).

More specifically, the unit vector of direction Y may be calculated asperpendicular to the calculated plane. The three rows of Z-constantpoints provide for determining the three lines best approximating themin the x,y,z system. The unit vector of direction X can be calculatedfrom the direction cosines of the “mean” of said lines, the term “meanline” referring to the line defined by the mean of the angles formed bythe three lines with each of the x,y,z system axes.

Finally, the unit vector of direction Z may be determined as the vectorproduct of the unit vectors of directions X and Y.

By the end of the procedure, the direction cosines of axes X, Y, Z inthe x,y,z system and hence the components of matrix R are thereforeknown (block 38).

2) Determining vector T by both units 4 and 5 measuring a fixed spherelocated at a point in the measuring volume.

Given the coordinates in both coordinate systems of a specific point inthe measuring volume, and given matrix R, the elements of vector T canbe determined from (1), by measuring the fixed sphere by means of unit(block 39) and unit 5 (block 40), and calculating vector T (block 41)from the sphere centre coordinates acquired in both reference systems.

By the end of this procedure, which is performed as part ofpost-installation setup of the machine, alignment of the referencesystems may be considered complete.

In actual fact, however, the components of matrix R and vector T mayvary over time with respect to those originally determined at themachine setup stage.

The rotation components may be affected by variations in the geometryand the mutual position of the machine arms—normally due to temperature,or yield caused by the workpiece load.

Foremost of the thermal factors affecting performance of multiple-armmachines is what is known as thermal drift, which causes deformation ofthe transducers and structural parts of the machine, in turn resultingin a shift in the points within the measuring volume. The amount ofshift depends not only on the amount of thermal stress applied, but alsoon the location of the point considered within the measuring volume.Such deformation produces variations in both matrix R and vector T.

As regards the workpiece load, this may produce significant variationsin pitch and roll, possibly differing from arm to the other, dependingon the more or less symmetrical position of the workpiece with respectto the arms.

To periodically update matrix R and vector T, a further calibration stepis required, prior to release of the machine to the user, and whichcomprises determining the position of sphere 25 with respect to arm 11(e.g. with respect to the flange centre). This is done by positioningsphere 25 at a point at intersection I of measuring volumes M1 and M2,where it can be detected by unit 5; and the coordinates reached by unit4 are memorized.

Sphere 25 is then measured by measuring tool 7 of unit 5, and thecoordinates of the centre of movable sphere 25 with respect to arm 11 ofunit 4 are calculated and memorized, thus giving the position of thecentre of sphere 25 on the basis of the machine coordinates of unit 4.

The above calibration step concludes setup of the machine. The referencesystem alignment updating procedures described below can be performed bythe user, do not require skilled personnel as in the case of the aboveprocedures, and, above all, do not involve prolonged, high-cost downtimeof the machine.

Alignment may be updated either fully (vector T and matrix R) orpartially, i.e. translational components only.

Full updating is recommended in the event of a significant change in theweight of the workpiece, or at the first shift of the week, or in theevent of significant variations in ambient temperature, and is aprobable once-weekly procedure.

Partial updating is recommended in the event of violent collisionbetween the measuring tool and workpiece, whenever the measuring toolstylus is changed for one of the same type, or in the event of mildvariations in ambient temperature, and is a probable once-dailyprocedure.

A) Updating Angular Alignment.

This procedure is described with reference to the FIG. 6 flow chart.

An automatic measuring cycle (blocks 43-47) is activated to measuremovable sphere 25 on unit 4 in k number of discrete positions atintersection I by means of unit 5. The number of positions may bedefined by the user, depending on the type of workpiece.

Block 49 calculates the angular alignment error Er in one or morepredetermined directions. If angular alignment errors below a firstthreshold are detected, units 4 and 5 are considered still properlyaligned, and the updating procedure is postponed (block 50).

If an angular alignment error is detected above a substantially highersecond threshold (S2) (block 51), measuring tool 7 of unit 5 is assumedno longer qualified, so the updating procedure is interrupted torequalify measuring tool 7 (block 53).

Finally, if an angular alignment error between the first and secondthreshold is detected, alignment is updated (block 52) by a proceduresimilar to the initial alignment procedure (movable sphere 25 is movedby unit 4 along a grid of points in a Y-constant plane and is measuredby unit 5; the unit vector defining direction Y is calculated asperpendicular to the plane approximating the acquired points; the unitvector of direction X is calculated from the lines interpolatingsuccessions of Z-constant points; and the unit vector of direction Z iscalculated as the vector product of the unit vectors defining directionsX and Y).

A residual rotation matrix R′ is thus calculated, and which is used tocorrect the memorized rotation matrix R (the new rotation matrix equalsthe residual rotation matrix multiplied by the memorized rotationmatrix).

B) Updating Translation Components.

This procedure is described with reference to the FIG. 7 flow chart.

The movable sphere (25) is positioned by unit 4 in one position atintersection I (block 56) and measured by unit 5 (block 58); the spherecentre coordinates are calculated (block 60); and the translation errorEt is calculated (block 61) as the difference between the sphere centrecoordinates calculated on the basis of the unit 5 measurements, and thesphere centre coordinates calculated on the basis of the positioncoordinates of unit 4.

If a translation error is detected below (in absolute value or withreference to each individual component) a first threshold S3 (block 62),units 4 and 5 are considered still properly aligned, and the updatingprocedure is postponed.

If a translation error is detected above a substantially higher secondthreshold (S4) (block 63), measuring tool 7 of unit 5 is assumed nolonger qualified, so the updating procedure is interrupted to requalifymeasuring tool 7 (block 65).

Finally, if a translation error between the first and second thresholdis detected, a vector T′ is calculated as the difference between thesphere centre coordinates measured by unit 5 and those resulting fromthe coordinates of unit 4, and is used to correct the memorized vector T(block 64). That is, the new (corrected) vector T equals the sum ofvector T′ and the memorized translation vector.

Both procedures A) and B) are performed for full updating, and onlyprocedure B) for partial updating.

The advantages of the method according to the present invention will beclear from the foregoing description.

In particular, alignment of the reference systems of units 4 and 5 canbe user-updated frequently, whenever called for by operatingcondition-affecting events (collision, variations in ambienttemperature, changing from one workpiece to another, etc.).

The updating procedure itself is fast, and involves no floor-mountedartifacts.

The method ensures a high degree of measuring precision of the machinealongside variations in ambient conditions, with no need for skilledlabour, and with no prolonged downtime of the machine.

Finally, because updating alignment of the reference systems providesfor compensating errors caused by yield of the bed or foundation whenthe workpiece is loaded, the bed and/or foundation may be made lighterwith no change in precision. In particular, the machine may be usedabove-ground, in which case, the foundation obviously cannot be overlyrigid for reasons of structural resistance of the building.

Clearly, changes may be made to the present invention without, however,departing from the scope of the accompanying Claims.

In particular, the machine may comprise more than two units, and theunits may be non-cartesian.

The updating procedure may be performed using different measuring tools,such as non-contact sensors. Finally, the initial alignment proceduremay be performed in any other known manner, e.g. by setting the fixedsphere successively to various positions at intersection I of measuringvolumes M1 and M2 of units 4 and 5, and determining the sphere centrecoordinates in the various positions by means of both units 4 and 5.Mathematically, if P_(i) and p_(i) are the positions measured in themaster and slave systems respectively, rotation matrix R is determinedby minimizing the error function:F=Σ _(i)(P _(i)−τ(R,T)p _(i))  (2)which may be done, for example, using the least squares method.Obviously, the better the approximation, the greater the number ofsphere positions i.

Alternatively, a complex artifact may be used, comprising, for example,a number of spheres in predetermined relative positions.

1. A method of aligning arm reference systems of a multiple-armmeasuring machine (1) comprising at least two measuring units (4, 5),each having a movable arm (11, 18), and a measuring tool (6, 7) movableby said arm (11, 18) in a respective measuring volume (M1, M2); themeasuring volumes (M1, M2) of said measuring units (4, 5) having anintersection (I), and defining as a whole a machine measuring volume (M)equal to the combined measuring volumes (M1, M2) of the individualmeasuring units; and the method comprising the steps of: fitting atleast one reference member (25) to the arm (11) of at least a firstmeasuring unit (4); qualifying each of said measuring tools (6, 7) ofthe respective measuring units (4, 5); aligning the reference systems(X,Y,Z; x,y,z) of said measuring units when setting up the machine (1);and periodically updating alignment of said reference systems bydetecting said reference member (25) by means of at least anothermeasuring unit (5); the reference member (25) being moved into a numberof positions at said intersection (I) by the first measuring unit (4).2. A method as claimed in claim 1, characterized in that said referencemember (25) is fixed rigidly to said arm (11) of said first measuringunit (4).
 3. A method as claimed in claim 2, characterized in that saidreference member (25) is a sphere.
 4. A method as claimed in claim 1,characterized by comprising the step of determining the position of saidreference member (25) with respect to said arm (11) of said firstmeasuring unit (4) by means of said other measuring unit (5).
 5. Amethod as claimed in claim 1, characterized in that said step ofupdating alignment of the reference systems comprises updating arotation matrix (R) and a translation vector (T).
 6. A method as claimedin claim 1, characterized in that said step of updating alignment of thereference systems comprises only updating a translation vector (T).
 7. Amethod as claimed in claim 1, characterized in that said updating stepcomprises performing an automatic measuring cycle, in which saidreference member (25) is positioned at said intersection (I) by saidfirst measuring unit (4) and measured by said other measuring unit (5).8. A method as claimed in claim 1, characterized in that said updatingstep is started upon detection of a residual error ranging between aminimum threshold value (S1; S3) and a maximum threshold value (S2; S4).